Compact Finite Difference Schemes for Mixed Initial-Boundary Value Problems - Philips, Richard B.; Rose, Milton E. (SIAM journal on numerical analysis, 1982)
This paper discusses a class of compact second order accurate finite difference equations for mixed initial-boundary value problems for hyperbolic and convective-diffusion equations. Convergence is proved by means of energy arguments and both types of equations are solved by similar algorithms. For hyperbolic equations an extension of the Lax-Wendroff method is described which incorporates dissipative boundary conditions. Upwind-downwind differencing techniques arise as the formal hyperbolic limit of the convective-diffusion equation. Finally, a finite difference "chain-rule" transforms the schemes from rectangular to quadrilateral subdomains.